IPA is one of the most important gradient estimation methods in the field of stochastic simulation [1]}. Based on [2]}, we can estimate the derivative of \(E\left[ {J\left( \theta \right)} \right]\)  using \(E\left[ {\frac{d}{{d\theta }}J\left( \theta \right)} \right]\) , where \({\frac{d}{{d\theta }}J\left( \theta \right)}\)  is known as the IPA estimator (or pathwise gradient estimator), if following conditions are satisfied:
